Sequencing of jobs on two and three machines...

1. Sequencing Problems
Abu Bashar

2. Sequencing???
• It is the selection of an appropriate order
in which a number of jobs (Operations)
can be assigned to to a finite number of
service facilities (Machines or equipments)
so as to optimize the outputs in terms of
time, cost or profit.

3. Common Sequencing Rules
• FCFS. First Come First Served. Jobs
processed in the order they come to the
shop.
• SPT. Shortest Processing Time. Jobs with
the shortest processing time are scheduled
first.
• EDD. Earliest Due Date. Jobs are sequenced
according to their due dates.
• CR. Critical Ratio. Compute the ratio of
processing time of the job and remaining
time until the due date. Schedule the job with
the largest CR value next.

4. Two Work Center Sequencing
• Johnson’s Rule: technique for minimizing
completion time for a group of jobs to be
processed on two machines or at two work
centers.
• Minimizes total idle time
• Several conditions must be satisfied

5. Johnson’s Rule Conditions
• Job time must be known and constant
• Job times must be independent of
sequence
• Jobs must follow same two-step sequence
• Job priorities cannot be used
• All units must be completed at the first
work center before moving to the second

6. Sequencing Problems
• One machine, many jobs
• Two machines, many jobs
• Three machines, many jobs
• Many machines, many jobs

7. One machine, many jobs
• Total time is independent of sequence
• Sequencing minimizes idle time

8. Two machines, many jobs
• All Jobs follow same sequence –
Johnson’s Rule
• Jobs have different sequence – Jackson’s
Rule
• Johnson’s 3 machine rule

9. Johnson’s Rule
• Johnson’s rule: A procedure that minimizes idle time
when scheduling a group of jobs on two workstations.
• Step 1. Find the shortest processing time among the
jobs not yet scheduled. If two or more jobs are tied,
choose one job arbitrarily.
• Step 2. If the shortest processing time is on workstation
1, schedule the corresponding job as early as possible.
If the shortest processing time is on workstation 2,
schedule the corresponding job as late as possible.
• Step 3. Eliminate the last job scheduled from further
consideration. Repeat steps 1 and 2 until all jobs have
been scheduled.

10. Eliminate M3 from consideration. The next shortest time
is M2 at Workstation 1, so schedule M2 first.
Eliminate M5 from consideration. The next shortest time is
M1 at workstation #1, so schedule M1 next.
Eliminate M1 and the only job remaining to be
scheduled is M4.
Example 16.5
Johnson’s RuleJohnson’s Rule at theat the Morris Machine Co.Morris Machine Co.
Time (hr)Time (hr)
MotorMotor Workstation 1Workstation 1 Workstation 2Workstation 2
M1M1 1212 2222
M2M2 44 55
M3M3 55 33
M4M4 1515 1616
M5M5 1010 88
Sequence =Sequence = M1M1M2M2 M3M3M4M4 M5M5
Shortest time is 3 hours at workstation 2, so
schedule job M3 last.
Eliminate M2 from consideration. The next shortest time is
M5 at workstation #2, so schedule M5 next to last.

11. Workstation
M2
(4)
M1
(12)
M4
(15)
M5
(10)
M3
(5)
Idle—available
for further work
0 5 10 15 20 25 30
Day
35 40 45 50 55 60 65
Idle2 M2
(5)
M1
(22)
M4
(16)
M5
(8)
M3
(3)Idle
1
Gantt Chart for the Morris Machine Company Repair Schedule
The schedule minimizes the idle time of workstation 2
and gives the fastest repair time for all five motors.
No other sequence will produce a lower makespan.
Example 16.5
Johnson’s RuleJohnson’s Rule at theat the Morris Machine Co.Morris Machine Co.

12. Problem
Job 1 2 3 4 5 6 7 8
A 4 5 8 10 6 5 10 6
B 8 10 2 4 5 7 6 6

13. Example

14. Johnson’s 3 Machine Rule
• Domination – Largest on B is not greater
than smallest on A or C. Domination
guarantees optimality
• Conversion – Convert into a 2 M/C
problem as M1 = A + B, M2 = B + C
• Find optimal sequence for this 2 machine
problem
• Schedule on 3 machines based on the
sequence above

15. Job 1 2 3 4 5 6
A 8 6 10 7 9 7
B 7 4 6 5 5 4
C 13 12 11 12 13 10
M1 15 10 16 12 14 11
M2 20 16 17 17 18 14
Classwork

16. j 1 2 3 4 5
tj1 8 11 7 6 9
tj2 3 2 5 7 11
tj3 6 5 7 13 10
Classwork

17. Thank You Very Much